Elements of Formal Semantics: An Introduction to the Mathematical Theory of Meaning in Natural Language

271 Pages·2016·2.45 MB·English

by  Yoad Winter

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mathematical principles that underlie linguistic meaning. Making use of a wide range of ticaa
concrete English examples, the book presents the most useful tools and concepts of l Thl An Introduction to the Mathematical
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formal semantics in an accessible style and includes a variety of practical exercises so ore Theory of Meaning in Natural Language
that readers can learn to utilise these tools effectively. For readers with an elementary y om
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mathematical study of meaning. N
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Yoad Winter is professor in Semantics and Artificial Intelligence at the Utrecht Institute r
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Cover design & illustration: riverdesign.co.uk
ISBN 978-0-7486-4043-0
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Edinburgh AdvAncEd TExTbooks in Linguistics
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Elements of Formal Semantics
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EdinburghAdvancedTextbooksinLinguistics
SeriesEditors
PeterAckema,ReaderinLinguistics(UniversityofEdinburgh)
MitsuhikoOta,ReaderinthePhoneticsandPhonologyofLanguage
Acquisition(UniversityofEdinburgh)
EditorialAdvisoryBoard
RicardoBermudez-Otero(UniversityofManchester)
KerstiBörjars(UniversityofManchester)
GrevilleCorbett(UniversityofSurrey)
AnastasiaGiannakidou(UniversityofChicago)
CarolineHeycock(UniversityofEdinburgh)
JackHoeksema(UniversityofGroningen)
MiriamMeyerhoff(UniversityofEdinburgh)
GeoffreyPullum(UniversityofEdinburgh)
AndrewSpencer(UniversityofEssex)
DoncaSteriade(MIT)
SusiWurmbrand(UniversityofConnecticut)
TITLESINTHESERIESINCLUDE
EssentialProgrammingforLinguistics
MartinWeisser
Morphology:FromDatatoTheories
AntonioFábregasandSergioScalise
LanguageandLogics:AnIntroductiontotheLogicalFoundations
ofLanguage
HowardGregory
ElementsofFormalSemantics:AnIntroductiontotheMathematical
TheoryofMeaninginNaturalLanguage
YoadWinter
VisittheEdinburghAdvancedTextbooksinLinguisticswebsiteat
www.euppublishing.com/series/EATL
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Elements of Formal Semantics
An Introduction to the Mathematical Theory
of Meaning in Natural Language
Yoad Winter
March8,2016 Time: 06:18pm prelims.tex
InmemoryofPaulaFrank-Boas
1916Amsterdam–2015Haifa
EdinburghUniversityPressisoneoftheleadinguniversitypressesintheUK.Wepublish
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(cid:2)cYoadWinter,2016
EdinburghUniversityPressLtd
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accordancewiththeCopyright,DesignsandPatentsAct1988,andtheCopyrightand
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CONTENTS
Acknowledgments vii
Notations ix
Abbreviations xi
1 Introduction 1
Aimsandorganizationofthisbook 4
Ontheexercisesinthisbook 6
Whoisthisbookfor? 6
Presupposedbackground 7
Fortheinstructor 7
Furtherreading,exercises,solutions 8
2 MeaningandForm 12
Entailment 12
ModelsandtheTruth-ConditionalityCriterion 17
Arbitraryandconstantdenotations 22
Analyzinganentailment 24
Directcompositionality 27
Structuralambiguity 30
Furtherreading,exercises,solutions 35
3 TypesandMeaningComposition 44
Part1:TypesandDomains 45
Part2:DenotationsatWork 52
Part3:UsingLambdaNotation 64
Part4:RestrictingDenotations 72
Furtherreading,exercises,solutions 90
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vi CONTENTS
4 QuantifiedNounPhrases 99
Generalizedquantifiersandthedenotationof
quantifiedNPs 101
Lookingatgeneralizedquantifiersinmodels 106
Quantifiermonotonicity 109
QuantifiedNPsandverbphrasecoordination 112
Determinerexpressions 114
Anoteonmonotonicityandnegativepolarityitems 122
Moreentailments,anddeterminerconservativity 124
CoordinationofquantifiedNPs 125
Propernamesandgeneralizedquantifiers 127
Furtherreading,exercises,solutions 131
5 Long-DistanceMeaningRelationships 139
Clauseswithmultiplenounphrases 141
HypotheticalreasoningandtheLambek-Van
BenthemCalculus 148
LinguisticsignsandAbstractCategorialGrammar 159
Usingsigns 167
Furtherreading,exercises,solutions 183
6 IntensionalityandPossibleWorlds 190
Puzzlesaboutintensionalexpressions 191
Extensions,intensionsandpossibleworlds 198
Intensionalityandgrammararchitecture 211
Dedicto/dereinterpretationsandscopeambiguity 218
Furtherreading,exercises,solutions 226
7 ConclusionandFurtherTopics 232
Recapitulation 232
Wheretogofromhere? 233
Moretopicsandreadingsinformalsemantics 234
AppendixtoChapter3 239
Bibliography 246
Index 253
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ACKNOWLEDGMENTS
This book has benefited from the generous feedback that I got over
the years from many colleagues and students. For their detailed
comments and extensive help, I am especially grateful to Philomena
Athanasiadou, Gilad Ben-Avi, Chris Blom, Sophie Chesney, Rogier
van Dinther, Gianluca Giorgolo, Eyal Hurvits, Theo Janssen, Heidi
Klockmann, Larry Moss, Kirsten Oosterom, Ya’acov Peterzil, Eddy
Ruys, Remko Scha, Assaf Toledo, Hanna de Vries and Joost Zwarts.
I am grateful to many other colleagues and students who have helped
myworkonthisbooksinceitsearlyversionstookshape.Iwouldalso
wishtothankananonymousEdinburghUniversityPressreviewer,as
well as the rest of the EUP team, for their help and patience during
the preparation of the manuscript. The quotation on page 1 appears
bykindpermissionof BD MusicCo. Workon this book was partially
supportedbyVICIgrant277-80-002oftheNetherlandsOrganisation
forScientificResearch(NWO),whichisgratefullyacknowledged.
Mostofall,IamgratefultoYaelandDanaSeggevandtherestofmy
family.Iwouldn’tfindanymeaningwithoutyou.
Utrecht,June2015
vii
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NOTATIONS
Forstandardset-theoreticalnotationseepages9and10.
* ungrammaticality
# semanticincoherence
(cid:2)
truth-valuefortrue
⊥
truth-valueforfalse
⇒
S S sentence S entailssentence S
1 2 1 2
(cid:2)
S S sentence S doesnotentailsentence S
1 2 1 2
⇔
S S sentences S and S areequivalent
1 2 1 2
(cid:3)
S S sentences S and S arenotequivalent
1 2 1 2
blik τ
τ arbitrarydenotationofawordblik,oftype
τ
BLIKτ constantdenotationofawordblik,oftype
[[exp]]M denotationofanexpressionexpinmodel M
ϕ τ ϕ τ
: denotation oftype
υ (cid:6)→ υ (cid:6)→ υ υ
[ r r ...] afunctionthatmaps tor , tor etc.
1 1 2 2 1 1 2 2
χ
thecharacteristicfunctionofasetY
Y
f* thesetcharacterizedbyafunction f
e typeofsemanticentities
t typeoftruth-values
f typeofphoneticentities
τ
Dτ domainoftype
FE frameoveranentitydomain E
E domainofsemanticentities(D )
e
F domainofphoneticentities(D )
f
ix